Mathlib Map

Theorems · Theorem

EmbeddingLike.injective

∀ {F : Sort u_1} {α : Sort u_2} {β : Sort u_3} [inst : FunLike F α β] [i : EmbeddingLike F α β] (f : F),
  Function.Injective ⇑f
Defined in
Mathlib.Data.FunLike.Embedding
Cited by
14 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
FunLikeEmbeddingLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Function.Embedding.injective · cited by 111Embedding.injectiveEquivLike.injective · cited by 32EquivLike.injectiveEmbeddingLike.apply_eq_iff_eq · cited by 20EmbeddingLike.apply_eq_if…EmbeddingLike.map_eq_zero_iff · cited by 9EmbeddingLike.map_eq_zero…EmbeddingLike.map_eq_one_iff · cited by 4EmbeddingLike.map_eq_one_…FirstOrder.Language.StrongHomClass.toEmbedding · cited by 4StrongHomClass.toEmbeddingEmbeddingLike.comp_injective · cited by 3EmbeddingLike.comp_inject…FirstOrder.Language.BoundedFormula.IsQF.realize_embedding · cited by 2IsQF.realize_embeddingEquiv.Perm.eq_top_of_isMultiplyPretransitive · cited by 1Perm.eq_top_of_isMultiply…Function.Bijective.addActionHom_embedding_isBijective · cited by 1Bijective.addActionHom_em…FirstOrder.Language.HomClass.strictMono · cited by 1HomClass.strictMonoFintype.card_range · cited by 1Fintype.card_rangeFunction.Bijective.mulActionHom_embedding_isBijective · cited by 1Bijective.mulActionHom_em…FirstOrder.Language.BoundedFormula.IsAtomic.realize_comp · cited by 0IsAtomic.realize_compEmbeddingLike.pairwise_comp · cited by 0EmbeddingLike.pairwise_co…DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeEmbeddingLike · cited by 20EmbeddingLikeEmbeddingLike.injective' · cited by 1EmbeddingLike.injective'EmbeddingLike.injectiveCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.